Summary: We consider two merit functions which can be used for solving the nonlinear complementarity problem via nonnegatively constrained minimization. One of the functions is the restricted implicit Lagrangian [

*M. Fukushima*, Mathematical Programming 53, 99-110 (1993;

Zbl 0756.90081),

*O. L. Mangasarian* and

*M. V. Solodov*, Mathematical Programming 62, 277-297 (1993;

Zbl 0813.90117),

*K. Taji* and

*M. Fukushima*, J. Oper. Res. Soc. Jap. 37, 310-331 (1994;

Zbl 0829.90125)], and the other appears to be new. We study the conditions under which a stationary point of the minimization problem is guaranteed to be a solution of the underlying complementarity problem. It appears that, for both formulations, the same regularity condition is needed. This condition is closely related to the one used by

*F. Facchinei* and

*C. Kanzow* [Technical Report A-97, Inst. Appl. Math., Univ. Hamburg, Germany (1995)] for unrestricted implicit Lagrangian. Some new sufficient conditions are also given.